Set in a dilapidated summer cabin in upstate New York, David Auburn’s engaging new play, Lost Lake, focuses on two people who might otherwise never have shared a stage. Yet Auburn, who won a Pulitzer Prize for Proof, develops a relationship between them that’s both believable and compelling. The result is a personal drama that resonates politically as well.

Veronica (Tracie Thoms) is a young black mother from New York City who, in the first scene, is negotiating the rent of a cabin for a week toward the end of summer. It’s March now, and Veronica has taken a bus to the cabin to inspect it personally and negotiate with the ostensible owner, Terry Hogan (John Hawkes). Hogan, shambling and pigeon-toed, is gregarious and optimistic but at times uncomfortably pushy, overselling the cabin (nicely detailed by J. Michael Griggs, with a broad upstage window and shabby plaid furniture). Yet Hogan also knows when he’s pushed too hard and needs to change the subject. But Veronica is no pushover, and Thoms invests her with the confidence and street smarts that make her unafraid to deal with Hogan.

When the summer week arrives, so does friction. Hogan hasn’t fixed the dock as he’d promised, and it’s rickety and dangerous for the children. He promised an extra bed; it’s not there. Worst, there’s no hot water. It’s a nightmare rental for Veronica, but Hogan tries to sell the bright side: “The kids are having a good time, right?” They bicker, and Auburn keeps one guessing where it’s all going. Daniel Sullivan’s superb production will make you want to stay along for the ride.

Sullivan deftly brings out the despair of these two lost souls. Their mistakes resonate with questions for the viewer. Is it possible to make a terrible mistake in one’s life and never be able to recover? Is there no chance for redemption? Hogan, it turns out, has a daughter from whom he is estranged, and a long record of failure. Veronica has a job that’s in jeopardy because of a mistake she has made, and is probably at the beginning of her decline. Auburn peels back layer after layer of their woes with astute dramatic timing. They are likable, flawed people trapped in limbo by their mistakes. The lake, a symbol of a carefree, pleasure-filled life, has been lost to them, perhaps forever.

It’s not all gloom. Hogan, slippery though he is, tries not to dwell on his misfortunes. Rather, he attempts to put a positive spin on Veronica’s troubles. No hot water? “I really don’t see how a few days of cold showers, which is good for the circulation by the way—you’re a nurse, you should know that—could be worth—how much did you say you wanted?” Hawkes delivers those lines with a brilliant balance of supplication and gall. Veronica has refused to pay the last installment of three days’ rent, but, Hogan argues, she hasn’t paid the installment so the water's being cold those first three days is immaterial.

There’s humor, too, in Hogan’s rants against his sister-in-law, Debbie, who, he claims, wants to squeeze him out of ownership of the cabin. Meanwhile, Thoms has a scene of physical comedy when she tries to get a cellphone signal. She holds up the cell; waves it; climbs on the window seats and stretches her arm up high. But the scene is also a physicalization of the characters’ predicament. Veronica and Hogan are literally out of touch with everyone else.

The homeowners’ organization, which represents lake residents but also, more broadly, society, wants Hogan out of their midst, isolated though he is already. And it’s unclear whether his good intentions led him to overextend himself by taking on the job of repairing the dock or whether he was a chump that the association took advantage of. But repairing the dock—and his life—is beyond his ability.

Hawkes, with his squinched, angular face, changes moods and emotions like a chameleon. Thoms has the more sympathetic role, and she handles herself admirably, restraining herself when she might justifiably explode, always trying to argue rationally, and becoming by turns exasperated and sympathetic. Lost Lake is a poignant portrait of America’s fringes, where an unforgiving society exiles its sinners.

Manhattan Theater Club presents Lost Lake through Dec. 21, with performance times varying week by week. Tickets and information are available by calling CityTix at 212-581-1212, online by visiting www.nycitycenter.org, or by visiting the box office at New York City Center, 131 West 55th St.